Today was the last day of mathematical analysis and Linear Algebra with Dan Witzner. Me and Florian did a lot of exercises with eignvalues and vectors. I guess I would take away that the procedure for finding eignenvalues for a 3x3 matrix involves solving a third-degree characteristic polynomial and I did not remember how to do that. My "memory path" for finding eigenvalues and their egenvectors:
1. Ax=λx -> (A-λI)x=0
2. This means that det(A-λI) must be 0, which leads us to the characteristic polynomium.
3. Solve the polynomium to find λ
4. for each λ find the linear combination that fulfills (A-λI)x=0
5. All linear combinations of the vector(s) found in 4 are eigenvectors belonging to λ.
In general I need to study these topics again before my exam:
SVD, Gram-shmidt, the advanced parts of the calculus corriculum.
1. Ax=λx -> (A-λI)x=0
2. This means that det(A-λI) must be 0, which leads us to the characteristic polynomium.
3. Solve the polynomium to find λ
4. for each λ find the linear combination that fulfills (A-λI)x=0
5. All linear combinations of the vector(s) found in 4 are eigenvectors belonging to λ.
In general I need to study these topics again before my exam:
SVD, Gram-shmidt, the advanced parts of the calculus corriculum.
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